Problem: Simplify the following expression: $a = \dfrac{24k - 12}{84k - 36}$ You can assume $k \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $24k - 12 = (2\cdot2\cdot2\cdot3 \cdot k) - (2\cdot2\cdot3)$ The denominator can be factored: $84k - 36 = (2\cdot2\cdot3\cdot7 \cdot k) - (2\cdot2\cdot3\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $a = \dfrac{(12)(2k - 1)}{(12)(7k - 3)}$ Dividing both the numerator and denominator by $12$ gives: $a = \dfrac{2k - 1}{7k - 3}$